Fuller is a free agent after his one-year deal at Charlton came to an end earlier this summer.
A host of Championship clubs are thought to be weighing up moves for the forward with the 33-year-old impressing at The Valley last season.
Charlton are one of the clubs keen to re-sign Fuller with the Jamaica international currently training with Chris Powell's side to maintain his fitness.
The former Stoke and Southampton man admits he would love to stay with the Addicks, but is open to offers as he weighs up all his options ahead of the new season.
"I would love to get something sorted out with Charlton as I have the utmost respect for the manager and a good relationship with the players, but at present they haven't proposed anything so I must consider all options," Fuller told Sky Sports.